TY - JOUR

T1 - Error estimation using hypersingular integrals in boundary element methods for linear elasticity

AU - Paulino, Glaucio H.

AU - Menon, Govind

AU - Mukherjee, Subrata

N1 - Funding Information:
G.H. Paulino acknowledges the support from the National Science Foundation under grant # CMS-9713008.

PY - 2001/7

Y1 - 2001/7

N2 - A natural measure of the error in the boundary element method rests on the use of both the standard boundary integral equation (BIE) and the hypersingular BIE (HBIE). An approximate (numerical) solution can be obtained using either one of the BIEs. One expects that the residual, obtained when such an approximate solution is substituted to the other BIE is related to the error in the solution. The present work is developed for vector field problems of linear elasticity. In this context, suitable 'hypersingular residuals' are shown, under certain special circumstances, to be globally related to the error. Further, heuristic arguments are given for general mixed boundary value problems. The calculated residuals are used to compute element error indicators, and these error indicators are shown to compare well with actual errors in several numerical examples, for which exact errors are known. Conclusions are drawn and potential extensions of the present error estimation method are discussed.

AB - A natural measure of the error in the boundary element method rests on the use of both the standard boundary integral equation (BIE) and the hypersingular BIE (HBIE). An approximate (numerical) solution can be obtained using either one of the BIEs. One expects that the residual, obtained when such an approximate solution is substituted to the other BIE is related to the error in the solution. The present work is developed for vector field problems of linear elasticity. In this context, suitable 'hypersingular residuals' are shown, under certain special circumstances, to be globally related to the error. Further, heuristic arguments are given for general mixed boundary value problems. The calculated residuals are used to compute element error indicators, and these error indicators are shown to compare well with actual errors in several numerical examples, for which exact errors are known. Conclusions are drawn and potential extensions of the present error estimation method are discussed.

KW - Boundary element methods

KW - Hypersingular integrals

KW - Linear elasticity

UR - http://www.scopus.com/inward/record.url?scp=0035399450&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035399450&partnerID=8YFLogxK

U2 - 10.1016/S0955-7997(01)00019-4

DO - 10.1016/S0955-7997(01)00019-4

M3 - Article

AN - SCOPUS:0035399450

VL - 25

SP - 523

EP - 534

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

IS - 7

ER -